1 radar basic -part i 1
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RADAR BasicsPart I
SOLO HERMELIN
Updated: 27.01.09Run This
http://www.solohermelin.com
Table of Content
SOLO Radar Basics
Introduction to RadarsBasic Radar Concepts
The Physics of Radio Waves Maxwell’s Equations:Properties of Electro-Magnetic WavesPolarizationEnergy and MomentumThe Electromagnetic Spectrum
Dipole Antenna RadiationInteraction of Electromagnetic Waves with Material
Absorption and Emission Reflection and Refraction at a Boundary Interface DiffractionAtmospheric Effects
Table of Content (continue – 1)
SOLO Radar Basics
Basic Radar Measurements
Radar Configurations
Range & Doppler Measurements in RADAR Systems
Waveform Hierarchy
Fourier Transform of a Signal
Continuous Wave Radar (CW Radar)
Basic CW Radar
Frequency Modulated Continuous Wave (FMCW)
Linear Sawtooth Frequency Modulated Continuous Wave
Linear Triangular Frequency Modulated Continuous Wave
Sinusoidal Frequency Modulated Continuous Wave
Multiple Frequency CW Radar (MFCW)
Phase Modulated Continuous Wave (PMCW)
Table of Content (continue – 2)
SOLO Radar Basics
Pulse Radars
Non-Coherent Pulse Radar
Coherent Pulse-Doppler Radar
Range & Doppler Measurements in Pulse-Radar SystemsRange Measurements
Range Measurement Unambiguity
Doppler Frequency Shift
Resolving Doppler Measurement Ambiguity
ResolutionDoppler Resolution
Angle Resolution
Range Resolution
Table of Content (continue – 3)
SOLO Radar Basics
Pulse Compression WaveformsLinear FM Modulated Pulse (Chirp)
Phase Coding
Poly-Phase Codes
Bi-Phase Codes
Frank Codes
Pseudo-Random Codes
Stepped Frequency Waveform (SFWF)
Table of Content (continue – 4)
SOLO Radar Basics
RF Section of a Generic Radar
Antenna
Antenna Gain, Aperture and Beam Angle
Mechanically/Electrically Scanned Antenna (MSA/ESA)
Mechanically Scanned Antenna (MSA)
Conical Scan Angular Measurement
Monopulse Antenna
Electronically Scanned Array (ESA)
Table of Content (continue – 5)
SOLO Radar Basics
RF Section of a Generic Radar
Transmitters
Types of Power Sources
Grid Pulsed Tube
Magnetron
Solid-State Oscillators
Crossed-Field amplifiers (CFA)
Traveling-Wave Tubes (TWT)
Klystrons
Microwave Power Modules (MPM)
Transmitter/Receiver (T/R) Modules
Transmitter Summary
RADAR
BASICS PART II
Table of Content (continue – 6)
SOLO Radar Basics
RF Section of a Generic Radar
Radar Receiver
Isolators/CirculatorsFerrite circulators
Branch- Duplexer
TR-Tubes
Balanced Duplexer
Wave Guides
Receiver Equivalent Noise
Receiver Intermediate Frequency (IF)Mixer Technology
Coherent Pulse-RADAR Seeker Block Diagram
RADAR
BASICS PART II
Table of Content (continue – 7)
SOLO Radar Basics
Radar Equation
Radar Cross Section
Irradiation
Decibels
Clutter
Ground Clutter
Volume Clutter
Multipath Return
RADAR
BASI
CS
PART
II
Table of Content (continue – 8)
SOLO Radar Basics
Signal Processing
Decision/Detection Theory
Binary Detection
Radar Technologies & Applications
References
RADAR
BASI
CS
PART
II
SOLO Radar Basics
The SCR-270 operating position shows the antenna positioning controls, oscilloscope, and receiver. Photo from "Searching The Skies"
A mobile SCR-270 radar set. On December 7, 1941, one of these sets detected Japanese aircraft approaching Pearl Harbor. Unfortunately, the detection was misinterpreted and ignored. Photo from "Searching The Skies"
SOLO Radar Basics
Limber Freya radar
Freya was an early warning radar deployed by Germany during World War II, named after the Norse Goddess Freyja. During the war over a thousand stations were built. A naval version operating on a slightly different wavelength was also developed as Seetakt. Freya was often used in concert with the primary German gun laying radar, Würzburg Riese ("Large Wurzburg"); the Freya finding targets at long distances and then "handing them off" to the shorter-ranged Würzburgs for tracking.
SOLO Radar Basics
Würzburg mobile radar trailer
The Würzburg radar was the primary ground-based gun laying radar for both the Luftwaffe and the German Army during World War II. Initial development took place before the war, entering service in 1940. Eventually over 4,000 Würzburgs of various models were produced. The name derives from the British code name for the device prior to their capture of the first identified operating unit.
In January 1934 Telefunken met with German radar researchers, notably Dr. Rüdolf Kuhnhold of the Communications Research Institute of the German Navy and Dr. Hans Hollmann, an expert in microwaves, who informed them of their work on an early warning radar. Telefunken's director of research, Dr. Wilhelm Runge, was unimpressed, and dismissed the idea as science fiction. The developers then went their own way and formed GEMA, eventually collaborating with Lorenz on the development of the Freya and Seetakt systems.
Country of origin GermanyIntroduced 1941Number built around 1500Range up to 70 km (44 mi)Diameter 7.5 m (24 ft 7 in)Azimuth 0-360ºElevation 0-90ºPrecision ±15 m (49 ft 2½ in)
SOLO Radar Basics
SOLO
Basic Radar Concepts
A RADAR transmits radio waves toward an area of interest and receives (detects) the radio waves reflected from the objects in that area.
RADAR: RAdio Detection And RangingRange to a detected object is determinate by the time, T, it takes the radio waves to propagate to the object and back
R = c T/2
Object of interest (targets) are detected in a background of interference.
Interference includes internal and external noise, clutter (objectsnot of interest), and electronic countermeasures..
Radar Basics
Radar BasicsSOLO
Radar BasicsSOLO
http://www.radartutorial.eu
Radar BasicsSOLO
SOLO
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Radar Basics
SOLO
The Physics of Radio Waves Electromagnetic Energy propagates (Radiates) by massless elementary “particles”known as photons. That acts as Electromagnetic Waves. The electromagnetic energy propagates in space in a wave-like fashion and yet can display particle-like behavior.
The electromagnetic energy can be described by:
• Electromagnetic Theory (macroscopic behavior)
• Quantum Theory (microscopic behavior)
Photon Properties
- There are no restrictions on the number of photons which can exist in a region with the same linear and angular momentum. Restriction of this sort (The Pauli Exclusion Principle) do exist for most other particles.
- The photon has zero rest mass (that means that it can not be in rest in any inertial system)- Energy of one photon is: ε = h∙f h = 6.6260∙10-34 W∙sec2 – Plank constant
f - frequency - Momentum of one photon is: p = m∙c = ε/c = h∙f/c
- The Energy transported by a large number of photons is, on the average, equivalent to the energy transferred by a classical Electromagnetic Wave.
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Radar Basics
SOLO
The Physics of Radio Waves Radio Waves are Electro-Magnetic (EM) Waves, Oscillating Electric and MagneticFields.
The Macroscopic properties of the Electro-Magnetic Field is defined by
Magnetic Field Intensity H [ ]1−⋅mA
Electric Displacement D [ ]2−⋅⋅ msA
Electric Field Intensity E [ ]1−⋅mV
Magnetic InductionB [ ]2−⋅⋅ msV
The relations between those quantities and the sources were derived by James Clerk Maxwell in 1861
James Clerk Maxwell(1831-1879)
1. Ampère’s Circuit Law (A) eJt
DH
+
∂∂=×∇
2. Faraday’s Induction Law (F) t
BE
∂∂−=×∇
3. Gauss’ Law – Electric (GE) eD ρ=⋅∇
4. Gauss’ Law – Magnetic (GM) 0=⋅∇ B
André-Marie Ampère1775-1836
Michael Faraday1791-1867
Karl Friederich Gauss1777-1855
Maxwell’s Equations:
Electric Current Density eJ
[ ]2−⋅mA
Free Electric Charge Distributioneρ [ ]3−⋅⋅ msA
zz
yy
xx
111:∂∂+
∂∂+
∂∂=∇
Radar Basics
SOLO Waves
2 2
2 2 2
10
d s d s
d x v d t− =Wave Equation
Regressive wave Progressive waverun this
-30 -20 -10
0.6
1.0.8
0.40.2
In the same way for a3-D wave
( ) ( )2 2 2 2 2
22 2 2 2 2 2 2
1 1, , , , , , 0
d s d s d s d s ds x y z t s x y z t
d x d y d z v d t v d t+ + − = ∇ − =
−=
v
xtfs
+=
v
xts ϕ
−=
−=
y
y
v
xtf
yd
d
td
sd
v
xtf
yd
d
vxd
sd
2
2
2
2
2
2
22
2
&1
+=
+=
z
z
v
xt
zd
d
td
sd
v
xt
zd
d
vxd
sd
ϕ
ϕ
2
2
2
2
2
2
22
2
&1
EM Wave
Equations
SOLO
ELECTROMGNETIC WAVE EQUATIONS
For Homogeneous, Linear and Isotropic MediumED
ε=
HB
µ=where are constant scalars, we haveµε ,
t
E
t
DH
t
t
H
t
BE
ED
HB
∂∂=
∂∂=×∇
∂∂
∂∂−=
∂∂−=×∇×∇
=
=
εµ
µ
ε
µ
Since we have also tt ∂
∂×∇=∇×∂∂
( )( ) ( )
=⋅∇=
∇−⋅∇∇=×∇×∇
=∂∂+×∇×∇
0&
0
2
2
2
DED
EEE
t
EE
ε
µε
t
DH
∂∂=×∇
t
BE
∂∂−=×∇
For Source-lessMedium
02
22 =
∂∂−∇
t
EE
µε
Define
meme KK
c
KKv ===
∆
00
11
εµµε
where ( )smc /103
1036
1104
11 8
9700
×=
××
==−−
∆
ππεµ
is the velocity of light in free space.
22
20
HH
tµε ∂∇ − =
∂
same way
The Physics of Radio Waves
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SOLO
Properties of Electro-Magnetic Waves
http://www.radartutorial.eu
Given a monochromatic (sinusoidal) E-M wave ( )0 0sin 2 sin
: /
xE E f t E t k x
c
k cω
π ω
ω
= − = − ÷ =
Period T,Frequency f = 1/T
Wavelength λ = c T =c/f c – speed of light
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POLARIZATION
SOLO
Electromagnetic wave in free space is transverse ; i.e. the Electric and Magnetic Intensitiesare perpendicular to each other and oscillate perpendicular to the direction of propagation.
A Planar wave (in which the Electric Intensity propagates remaining in a plane – containing the propagation direction) is said to be Linearly Polarized or Plane-Polarized.
If EM wave composed of two plane waves of equal amplitude but differing in phase by 90° then the EM wave is said to be Circular Polarized.
If EM wave is composed of two plane waves of different amplitudes and/or the difference in phase is different than 0,90,180,270° then the light is aid to be Elliptically Polarized.
If the direction of the Electric Intensity vector changes randomly from time to time we say that the EM wave is Unpolarized.
E
Properties of Electro-Magnetic Waves
See “Polarization” presentation for more details
POLARIZATION
SOLO
A Planar wave (in which the Electric Intensity propagates remaining in a plane – containing the propagation direction) is said to be Linearly Polarized or Plane-Polarized.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
http://www.enzim.hu/~szia/cddemo/edemo0.htm (Andras Szilagyi(
Linear Polarization or Plane-Polarization
( ) yyzktj
y eAE 1∧
+−= δω
Properties of Electro-Magnetic Waves
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POLARIZATION
SOLO
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
If EM wave is composed of two plane waves of equal amplitude but differing in phase by 90° then the light is said to be Circular Polarized.
http://www.optics.arizona.edu/jcwyant/JoseDiaz/Polarization-Circular.htm
( ) ( ) yx xx zktjzktj eAeAE 11 2/∧
++−∧
+− += πδωδω
Properties of Electro-Magnetic Waves
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POLARIZATION
SOLO Properties of Electro-Magnetic Waves
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SOLO
Energy and Momentum
Let start from Ampère and Faraday Laws
∂∂−=×∇⋅
+∂∂=×∇⋅−
t
BEH
Jt
DHE e
EJt
DE
t
BHHEEH e
⋅−
∂∂⋅−
∂∂⋅−=×∇⋅−×∇⋅
( )HEHEEH
×⋅∇=×∇⋅−×∇⋅But
Therefore we obtain
( ) EJt
DE
t
BHHE e
⋅−
∂∂⋅−
∂∂⋅−=×⋅∇
This theorem was discovered by Poynting in 1884 and later in the same year by Heaviside.
ELECTROMAGNETICS
John Henry Poynting1852-1914
Oliver Heaviside1850-1925
SOLO
Energy and Momentum (continue -1)
We identify the following quantities
- Power density of the current density [watt/m2[ EJ e
⋅
( )1 1
2 2e
m e
J E H B E D E Ht t
w wS
t t
∂ ∂ × = − × − × −∇× × ÷ ÷∂ ∂ ∂ ∂= − − −∇×
∂ ∂
⋅
∂∂=⋅= BHt
pBHw mm
2
1,
2
1
⋅
∂∂=⋅= DEt
pDEw ee
2
1,
2
1
( )Rp E H S= ∇ × × = ∇ ×
eJ
- Magnetic energy and power densities, respectively [watt/m2[
- Electric energy and power densities, respectively [watt/m2[
- Radiation power density [watt/m2[
For linear, isotropic electro-magnetic materials we can write ( )HBED
00 , µε ==
( )DEtt
DE
ED
⋅∂∂=
∂∂⋅
=
2
10ε
( )BHtt
BH
HB
⋅∂∂=
∂∂⋅
=
2
10µ
Umov-Poynting vector(direction of E-M
energy propagation)
:S E H= ×
John Henry Poynting1852-1914
Nikolay Umov1846-1915 S
E
H
( ) EJt
DE
t
BHHE e
⋅−
∂∂⋅−
∂∂⋅−=×⋅∇
ELECTROMAGNETICS
SOLO
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- Power density of the current density [watt/m2[ EJ e
⋅
⋅
∂∂=⋅= BHt
pBHw mm
2
1,
2
1
⋅
∂∂=⋅= DEt
pDEw ee
2
1,
2
1
( )Rp E H S= ∇ × × = ∇×
eJ
- Magnetic energy and power densities, respectively [watt/m2[
- Electric energy and power densities, respectively [watt/m2[
- Radiation power density [watt/m2[
Energy and Momentum (continue -2)
St
w
t
wEJ em
e
⋅∇−
∂∂−
∂∂−=⋅
EnergyRadiated
S
EnergyElectric
V
e
EnergyMagnetic
V
m
EnergySupplied
V
e
VV
e
V
m
V
e
dsSdvwt
dvwt
dvEJ
dvSdvwt
dvwt
dvEJ
∫∫∫∫∫∫∫∫∫∫∫
∫∫∫∫∫∫∫∫∫∫∫∫
⋅+∂∂+
∂∂+⋅=
⋅∇+∂∂+
∂∂+⋅=0
∫∫∫ ⋅V
e dvEJ
∫∫∫∂∂
V
mdvwt
∫∫∫∂∂
V
edvwt ∫∫ ⋅
S
dsS
Conservation of Energy
Integration over
a finite volume V
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SOLO
The Electromagnetic Spectrum
SOLO
SOLO
SOLO
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SOLO
( ) ( ) φφ ωω θπ
θπω
πω
11 0
2
0
2
2sin1
4sin
44
∧−
∧−
−−=
−= krtjkrtj ep
rk
j
r
kcep
rcr
jH
( )krtjepr
k
r
kj
r
rccrj
rE
r
rr
−∧∧∧
∧∧∧∧∧
−
+
+=
−+++=
ωθθ
θθθ
θθθπε
πεθω
πεθθω
πεθθ
0
2
23
0
2
0
2
2
0
3
0
111
11111
sinsincos21
4
1
4
sin
4
sincos2
4
sincos2
We can divide the zones around the source, as function of the relation between dipole size d and wavelength λ, in three zones:
Near, Intermediate and Far Fields
The Magnetic Field Intensity is transverse to the propagation direction at all ranges, but the Electric Field Intensity has components parallel and perpendicular to .r1
∧r1∧
E
However and are perpendicular to each other.H
• Near (static) zone: λ<<<< rd
• Intermediate (induction) zone: λ~rd <<
• Far (radiation) zone: rd <<<< λ
Antenna Radiation
Given a Short Wire Antenna. The antenna is oriented along the z axis with its center at thecenter of coordinate system. The current density phasor through the antenna is
( ) ( ) zSS
tjmSe rre
A
Itrj 10,
∧
−=
δω
See “Antenna Radiation” Presentation, Tildocs # 761172 v1
SOLO Electric Dipole RadiationPoynting Vector of the Electric Dipole Field
The Total Average Radiant Power is:
( )∫∫
==
π
θθπθεπω
0
22
23
0
2
42
0 sin2sin42
drrc
pdSSP
Arad
20
22
120123
0
420
3/4
0
323
0
420 40
12sin
160
prc
pd
rc
pP
c
c
rad
===
=
=∫ λ
πεπωθθ
επω λ
πω
πε
π
( ) ( )3
4
3
2
3
2cos
3
1coscoscos1sin
0
30
2
0
3 =
−−=
−=−= ∫∫
ππ
π
θθθθθθ dd
HES
×=:
The Poynting Vector of the Electric Dipole Field is given by:
The time average < > of the Poynting vector is: ( )∫→∞=
T
TdttS
TS
0
1lim
( ) rrc
pS 12
23
0
2
42
0 sin42
∧
−= θεπω
For the Electric Dipole Field:
SOLO Electric Dipole RadiationRadiance Resistence
222
0
2
28080
21
LI
p
I
PR
mm
radrad
=
==
λπ
λπ
Average Radiance
22
20
2
20
2
210
4
40
4 r
p
r
p
r
PS rad
avgr λπ
πλπ
π=
==
Gain of Dipole Antenna
θ
λπ
θλ
π2
22
20
222
20
sin2
3
10
sin15===
r
p
r
p
S
SG
avgr
r
Therefore
Gr
PGSS rad
avgrr 24π== Radar Equation
SOLO Electric Dipole Radiation
http://dept.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_apr_07_2003.shtml#tth_sEc12.1 http://www.falstad.com/mathphysics.html
Electric Field Lines of Force (continue -4)
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SOLO Antenna
Field Regions Relative to Antenna
SOLO
SOLO
ElectromagnetismSOLO
In 1888 Heinrich Hertz, created in Kieln Germany a device that transmitted and received electromagnetic waves.
1888
Heinrich Rudolf Hertz1857-1894
His apparatus had a resonant frequency of 5.5 107 c.p.s.
Aircapacitor
Hertz also showed that the waves could be reflected by a wall, refracted by a pitch prism, and polarized by a wire grating. This proved that the electromagnetic waves had the characteristics associated with visible light.
http://en.wikipedia.org/wiki/Heinrich_Hertz
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SOLO Interaction of Electromagnetic Waves with Material
• Reflection
• Refraction
• Diffraction
- the re-radiation (scattering) of EM waves from the surface of material
- the bending of EM waves at the interface of two materials
-the bending of EM waves through an aperture in, or around an edge, of a material
• Absorption- the absorption of EM energy is due to the interaction with the material
Stimulated Emission& Absorption
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SOLO Absorption and Emission
The absorption of a photon of frequency ν by a medium corresponds to the destruction of the photon; by conservation of energy the absorbing medium must be excited to alevel with energy h ν1 > h ν0 .
Stimulated Emission& Absorption Photon emission corresponds to the creation of a photon of
frequency ν; by conservation of energy, the emitting medium must be de-excited from an excited state to a state of lower energy than the excited state h ν = h ν2 - h ν1.
Phenomenologically, absorption and emission in gas phase media composed of atoms, diatomic molecules, and even larger molecules are restricted to discrete frequencies corresponding to the difference in the energy levels in the atoms. Continuous frequencies regimes arise only when the absorbed electromagnetic frequency is sufficiently high to ionize the atoms or molecules.
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SOLO Reflection and Refraction at a Boundary Interface
When an electromagnetic wave of frequency ω=2πf is traveling through matter, the electrons in the medium oscillate with the oscillation frequency of the electromagnetic wave. The oscillations of the electrons can be described in terms of a polarization of the matter at the incident electromagnetic wave. Those oscillations modify the electric field in the material. They become the source of secondary electromagnetic wave which combines with the incident field to form the total field.
The ability of matter to oscillate with the electromagnetic wave of frequency ω is embodied in the material property known as the index of refraction at frequency ω, n (ω).
SOLO Refraction at a Boundary Interface
• If EM wavefronts are incident to a material surface at an angle, then the wavefronts will bend as they propagate through the material interface. This is called refraction.
• Refraction is due to change in speed of the EM waves when it passes from one material to another.
Index of refraction: n = c / v
Snell’s Law: n1 sin θ1 = n2 sin θ2
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SOLO Reflection at a Boundary Interface
• Incident EM waves causes charge in material to oscillate, and thus, re-radiates (scatters) the EM waves.
• If the charge is free (conductor), all the EM – wave energy is essentially re-radiated.
• If the charge is bound (dielectric), some EM – wave energy is re-radiated and some propagates through the material.
SOLO
Scattering Mechanism
SOLOGeneric Aircraft Model Scattering Center
SOLOGeneric Aircraft Model Scattering Center
SOLOMultiple Bounce Specular Mechanism
SOLO Wave Propagation Summary (continue)• Surface Diffraction- increases at lower frequency, range, and higher surface roughness
• Surface Multipath
• Surface Intervisibility
- increases at lower frequency, range, and lower surface roughness. Also present at high frequencies for smooth terrain type (asphalt, low sea state, desert sand, clay,…)
If surface roughness dimension is much less than wavelength, λ, of EM waves, then scattering is specular, otherwise, scattering is diffuse.
SOLO
• Path difference of the two rays is Δr = 2 h sin γ
• Similarly the phase difference (Δφ) is simply k Δr or 4 π h sin γ / λ
• By arbitrarily setting the phase difference to be less than π /2 we obtain the Rayleigh criteria for “rough surface”
Other criteria such as phase difference less than π /4 or π /8 are considered more realistic.
Rayleigh Roughness Criteria(Multipath/Roughness)
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SOLO
• EM waves will propagate isotropically (Huygen’s Principle) unless prevented to do so by wave interference.
Diffraction
SOLO
• for a circular aperture antenna of diameter D, the half-intensity (3-dB) angular extent of the diffraction “pattern” is given by:
Radar DiffractionAntenna Beam-Width (Diffraction Limit)
degreesD
radiansDB
λλθ 7022.1 ==
We can see that to getImaging Resolution ofcentimeters, at 10 km,we need either optical wavelength λ of micro-meters for apertureD of order of foots orif we use microwavesλ = 3 cm we need anAperture of order ofD ~ 32 km
Resolution cells at a range of 10 kmResolution cells at a range of 10 km
SOLO Radar DiffractionAntenna Beam-Width (Diffraction Limit)
We saw (previous slide) that to get Imaging Resolution of centimeters, at 10 km, we need either optical wavelength λ of micro-meters for aperture D of order of foots orif we use microwaves λ = 3 cm we need an Aperture of order of D ~ 32 km.
For this reason most of Radar Applications deal with blobs of energy returns, not with imaging.
SOLO Radar DiffractionAntenna Beam-Width (Diffraction Limit)
To obtain Imaging at Radar Frequencies we must Synthesize a Large Aperture Antenna, using signal processing. Synthetic Aperture Radar (SAR) is a techniqueof “synthesizing” a large antenna (D) by moving a small antenna over some distance,collecting data during the motion, and processing the data to simulate the results froma large aperture.
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SOLO Atmospheric Effects
• Atmospheric Absorption
- increases with frequency, range, and concentration of atmospheric particles (fog, rain drops, snow, smoke,…)
• Atmospheric Refraction
- occurs at land/sea boundaries, in condition of high humidity, and at night when a thermal profile inversion exists, especially at low frequencies.
• Atmospheric Turbulence
- in general at high frequencies (optical, MMW or sub-MMW), and is strongly dependent on the refraction index (or temperature) variations, and strong winds.
SOLO
• The index of refraction, n, decreases with altitude.
• Therefore, the path of a horizontally propagating EM wave will gradually bend towards the earth.
• This allows a radar to detect objects “over the horizon”.
Atmospheric Effects (continue – 1)
SOLO Sun, Background and Atmosphere (continue – 2)
Atmosphere
Atmosphere affects electromagnetic radiation by
( ) ( )3.2
11
==
RkmRR ττ
• Absorption • Scattering • Emission • Turbulence
Atmospheric Windows:
Window # 2: 1.5 μm ≤ λ < 1.8 μm
Window # 4 (MWIR): 3 μm ≤ λ < 5 μm
Window # 5 (LWIR): 8 μm ≤ λ < 14 μm
For fast computations we may use the transmittance equation:
R in kilometers.
Window # 1: 0.2 μm ≤ λ < 1.4 μmincludes VIS: 0.4 μm ≤ λ < 0.7 μm
Window # 3 (SWIR): 2.0 μm ≤ λ < 2.5 μm
SOLO
Sun, Background and Atmosphere (continue – 3)
SOLO Sun, Background and Atmosphere (continue – 4)
Atmosphere Absorption over Electromagnetic Spectrum
SOLO Sun, Background and Atmosphere (continue – 5)
Rain Attenuation over Electromagnetic Spectrum
FREQUENCY GHz
ON
E-W
AY
AT
TE
NU
AT
ION
-Db
/KIL
OM
ET
ER
WAVELENGTH
Return to Table of contents
SOLO
Basic Radar Measurements
Radar makes measurements in five dimensional-space
• two (orthogonal) angular axes (θ, φ)
• range
• Doppler (frequency)
• polarization
Target information determined by the radar
• size (RCS) - from received power of electromagnetic waves
• range - from time-delay of electromagnetic waves
• angular position - from antenna pointing angles (θ, φ)
• speed (radial) - from received electromagnetic waves frequency
• identification - from amplitude (imagery), frequency, and polarization of electromagnetic waves
Target
Range
Ground
A.C RADAR
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SOLO Radar Configurations
Monostatic (Collocated) Antennas Bistatic Antennas
SOLO Radar Configuration
antenna
target
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Run This
Range & Doppler Measurements in RADAR SystemsSOLO
The transmitted RADAR RF Signal is:
( ) ( ) ( )[ ]ttftEtEt 0000 2cos ϕπ +=E0 – amplitude of the signal
f0 – RF frequency of the signal φ0 –phase of the signal (possible modulated)
The returned signal is delayed by the time that takes to signal to reach the target and toreturn back to the receiver. Since the electromagnetic waves travel with the speed of lightc (much greater then RADAR andTarget velocities), the received signal is delayed by
c
RRtd
21 +≅
The received signal is: ( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos
To retrieve the range (and range-rate) information from the received signal thetransmitted signal must be modulated in Amplitude or/and Frequency or/and Phase.
ά < 1 represents the attenuation of the signal
Range & Doppler Measurements in RADAR SystemsSOLO
The received signal is:
( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos
( ) ( ) tRRtRtRRtR ⋅+=⋅+= 222111 &
We want to compute the delay time td due to the time td1 it takes the EM-wave to reachthe target at a distance R1 (at t=0), from the transmitter, and to the time td2 it takes the EM-wave to return to the receiver, at a distance R2 (at t=0) from the target. 21 ddd ttt +=
According to the Special Relativity Theorythe EM wave will travel with a constant velocity c (independent of the relative velocities ).21 & RR
The EM wave that reached the target at time t was send at td1 ,therefore
( ) ( ) 111111 ddd tcttRRttR ⋅=−⋅+=− ( )1
111 Rc
tRRttd
+⋅+=
In the same way the EM wave received from the target at time t was reflected at td2 , therefore
( ) ( ) 222222 ddd tcttRRttR ⋅=−⋅+=− ( )2
222 Rc
tRRttd
+⋅+=
SOLO
The received signal is:
( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos
21 ddd ttt += ( )1
111 Rc
tRRttd
+⋅+= ( )
2
222 Rc
tRRttd
+⋅+=
( ) ( )2
22
1
1121 Rc
tRR
Rc
tRRtttttttt ddd
+⋅+−
+⋅+−=−−=−
From which:
+
−+−+
+
−+−=−
2
2
2
2
1
1
1
1
2
1
2
1
Rc
Rt
Rc
Rc
Rc
Rt
Rc
Rctt d
or:
Since in most applications we canapproximate where they appear in the arguments of E0 (t-td), φ (t-td),however, because f0 is of order of 109 Hz=1 GHz, in radar applications, we must use:
cRR <<21,
1,2
2
1
1 ≈+−
+−
Rc
Rc
Rc
Rc
( )
−⋅
++
−⋅
+=
−⋅
−⋅+
−⋅
−⋅≈− 2
.
201
.
1022
011
00 2
1
2
1
2
121
2
121
21
D
RalongFreqDoppler
DD
RalongFreqDoppler
Dd ttffttffc
Rt
c
Rf
c
Rt
c
Rfttf
where 212
21
1212
021
01 ,,,,2
,2
dddddDDDDD tttc
Rt
c
Rtfff
c
Rff
c
Rff +=≈≈+=−≈−≈
( ) ( ) ( ) ( ) ( )[ ] ( )tnoisettttffttEtE ddDdr +−+−+−= ϕπα 00 2cosFinally
Matched Filters in RADAR Systems
Doppler Effect
SOLO
The received signal model:
( ) ( ) ( ) ( ) ( )[ ] ( )tnoisettttffttEtE ddDdr +−+−+−= ϕπα 00 2cos
Matched Filters in RADAR Systems
Delayed by two-way trip time
Scaled downAmplitude Possible phase
modulated
CorruptedBy noise
Dopplereffect
We want to estimate:
• delay td range c td/2
• amplitude reduction α
• Doppler frequency fD
• noise power n (relative to signal power)
• phase modulation φ
2-Way Doppler Shift Versus Velocity and Radio Frequency SOLO
Doppler Frequency Shifts (Hz) for Various Radar Frequency Bands and Target Speeds
Band 1 m/s 1 knot 1 mph
L (1 GHz)S (3 GHz)C (5 GHz)X (10 GHz)
Ku (16 GHz)Ka (35 GHz)
mm (96 GHz)
6.6720.033.366.7107233633
3.4310.317.134.354.9120320
2.988.9414.929.847.7104283
RadarFrequency Radial Target Speed
SOLO
Return to Table of contents
SOLO Waveform Hierarchy
Radar Waveforms
CW Radars Pulsed Radars
FrequencyModulated CW
PhaseModulated CW
bi – phase & poly-phase
Linear FMCWSawtooth, or
Triangle
Nonlinear FMCWSinusoidal,
Multiple Frequency,Noise, Pseudorandom
Intra-pulse Modulation
Pulse-to-pulse Modulation,
Frequency AgilityStepped Frequency
FrequencyModulate Linear FM
Nonlinear FM
PhaseModulatedbi – phase poly-phase
Unmodulated CW
Multiple FrequencyFrequency
Shift Keying
Fixed Frequency
Range & Doppler Measurements in RADAR SystemsSOLO
( )tf
2
τ2
τ−
A
∞→t
2τ+T
2τ−T
A
2
τ+−T2
τ−−T
A
t←∞−
T TA
t
A
t
A
LINEAR FM PULSECODED PULSE
T T
PULSED (INTRAPULSE CODING)
t
( )tf
A
2
τ2
τ−T
AA
T T
A
22
τ+T2
2τ−T
A
T T
A
2
τ− 2
τ+T
TN
t
( )tf
A
2
τ2
τ−T
AA
T T
A
22
τ+T2
2τ−T
A
T T
A
2
τ− 2
τ+T
TN
PHASE CODED PULSES HOPPED FREQUENCY PULSES
PULSED (INTERPULSE CODING)
( )tf
2
τ2
τ−
A
∞→t
2
τ+T2
τ−T
A
2
τ+−T2
τ−−T
A
t←∞−
T T
NONCOHERENT PULSESCOHERENT PULSES
( )tf
t
A
2
τ2
τ−T
AA
T T
A
22
τ+T2
2τ−T
A
T T
A
2
τ− 2
τ+T
TN
PULSED (UNCODED)
t
( )tf
A
T
2/τ−
LOW PRFMEDIUM PRF
PULSED( )tf
T T T T
2/τ+
τ
HIGH PRF
TT T T
A Partial List of the Family of RADAR Waveforms
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SOLO Fourier Transform of a Signal
The Fourier transform of a signal f (t) can be written as:
A sufficient (but not necessary) condition for theexistence of the Fourier Transform is:
( ) ( ) ∞<= ∫∫∞
∞−
∞
∞−
ωωπ
djFdttf22
2
1
JEAN FOURIER1768-1830
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
The Inverse Fourier transform of F (j ω) is given by:
( ) ( )∫+∞
∞−
= dtetfjF tjωω
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
Signal
(1) C.W.
( )2
cos00
0
tjtj eeAtAtf
ωω
ω−+==
0ω - carrier frequency
Frequency
( ) ( )∫+∞
∞−
= dtetfjF tjωωFourier Transform
( ) ( ) ( )00 22ωωδωωδω ++−= AA
jFFourier Transform
SOLO Fourier Transform of a Signal
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
Signal
(2) Single Pulse
( )
>≤≤−
=2/0
2/2/
τττ
t
tAtf
τ - pulse width
Frequency
( ) ( )∫+∞
∞−
= dtetfjF tjωωFourier Transform
( ) ( ) ( )( )2/
2/sin2/
2/ τωτωτω
τ
τ
ω AdteAjF tj == ∫−
Fourier Transform
SOLO Fourier Transform of a Signal
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
Signal
( ) ( )
>≤≤−
=2/0
2/2/cos 0
τττω
t
ttAtf
τ - pulse width
Frequency
( ) ( )∫+∞
∞−
= dtetfjF tjωωFourier Transform
( ) ( )
( )
( )
( )
( )
−
−
++
+
=
= ∫−
2
2sin
2
2sin
2
cos
0
0
0
0
2/
2/
0
τωω
τωω
τωω
τωωτ
ωωτ
τ
ω
A
dtetAjF tjFourier Transform
0ω - carrier frequency
(3) Single Pulse Modulated at a frequency
0ω
ω
( )ωjF
0
τπω 2
0 +
2
τA
0ω
τπω 2
0 −τπω 2
0 +−
2
τA
0ω−
τπω 2
0 −−
τπω 2
20 +τπω 2
20 −
SOLO Fourier Transform of a Signal
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
Signal
( ) ( )
±±=>−≤−≤−+
=,2,1,0,2/0
2/2/cos 0
kkkTt
kTttAtf
rand
τττϕω
τ - pulse width
Frequency
( ) ( )∫+∞
∞−
= dtetfjF tjωωFourier Transform
( ) ( )
( )
( )
( )
( )
−
−
++
+
=
= ∫−
2
2sin
2
2sin
2
cos
0
0
0
0
2/
2/
0
τωω
τωω
τωω
τωωτ
ωωτ
τ
ω
A
dtetAjF tj
Fourier Transform
0ω - carrier frequency
(4) Train of Noncoherent Pulses (random starting pulses), modulated at a frequency 0ω
T - Pulse repetition interval (PRI)
SOLO Fourier Transform of a Signal
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
Signal
( ) ( )
( ) ( )( ) ( )( )[ ]
−++
+=
±±=>−≤−≤−
=
∑∞
=1000
0
coscos
2
2sin
cos
,2,1,0,2/0
2/2/cos
nPRPR
PR
PRseriesFourier
tntnn
n
tT
A
kkkTt
kTttAtf
ωωωωτω
τω
ωτ
τττω
τ - pulse width
Frequency
( ) ( )∫+∞
∞−
= dtetfjF tjωωFourier Transform
Fourier Transform
0ω - carrier frequency
(5) Train of Coherent Pulses, of infinite length, modulated at a frequency 0ω
T - Pulse repetition interval (PRI)
( ) ( ) ( ){
( ) ( ) ( ) ( )[ ]
+−+−+−−++
+
−+=
∑∞
= 10000
00
2
2sin
2
nPRPRPRPR
PR
PR
nnnnn
n
T
AjF
ωωδωωδωωδωωδτω
τω
ωδωδτω
T/1 - Pulse repetition frequency (PRF)TPR /2πω =
SOLO Fourier Transform of a Signal
( ) ( )∫+∞
∞−
−= ωωπ
ω dejFj
tf tj
2
1
Signal
( ) ( )
( ) ( )( ) ( )( )[ ]
−++
+=
±±=>−≤−≤−
=
∑∞
=
≤≤−
1000
22
0
coscos
2
2sin
cos
2/,,2,1,0,2/0
2/2/cos
nPRPR
PR
PRNTt
NT
tntnn
n
tT
A
NkkkTt
kTttAtf
ωωωωτω
τω
ωτ
τττω
τ - pulse width
Frequency
( ) ( )∫+∞
∞−
= dtetfjF tjωωFourier Transform
Fourier Transform
0ω - carrier frequency
(6) Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω
T - Pulse repetition interval (PRI)
( )( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
−−
−−
++−
+−
++
+
+
−+
−+
+++
++
++
+
=
∑
∑
∞
=
∞
=
10
0
0
0
0
0
10
0
0
0
0
0
2
2sin
2
2sin
2
2sin
2
2sin
2
2sin
2
2sin
2
2sin
2
2sin
2
nPR
PR
PR
PR
PR
PR
nPR
PR
PR
PR
PR
PR
TNn
TNn
TNn
TNn
n
n
TN
TN
TNn
TNn
TNn
TNn
n
n
TN
TN
T
AjF
ωωω
ωωω
ωωω
ωωω
τω
τω
ωω
ωω
ωωω
ωωω
ωωω
ωωω
τω
τω
ωω
ωωτω
T/1 - Pulse repetition frequency (PRF)TPR /2πω =
SOLO Fourier Transform of a Signal
Signal
( ) ( )
+=
±±=>−≤−≤−
= ∑∞
=11 cos
2
2sin
21,2,1,0,2/0
2/2/
nPR
PR
PRSeriesFourier
tnn
n
T
AkkkTt
kTtAtf ω
τω
τωτ
τττ
τ - pulse width0ω - carrier frequency
(6) Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω
T - Pulse repetition interval (PRI)
T/1 - Pulse repetition frequency (PRF)TPR /2πω =
( ) ( )tAtf 03 cos ω=
t
A A
( )tf1
t
2
τ2
τ−T
A
T T
22
τ+T
22
τ−T
T T
2
τ− 2
τ+T
( )tf 2
t
TN
2/TN2/TN−
( ) ( ) ( ) ( )tftftftf 321 ⋅⋅=
( ) ( ) ( ) ( ) ( )
( ) ( )( ) ( )( )[ ]
−++
+=
±±=>−≤−≤−
=⋅⋅=
∑∞
=
≤≤−
1000
22
0
321
coscos
2
2sin
cos
2/,,2,1,0,2/0
2/2/cos
nPRPR
PR
PRNTt
NT
tntnn
n
tT
A
NkkkTt
kTttAtftftftf
ωωωωτω
τω
ωτ
τττω
( )
>≤≤−
=2/0
2/2/12 TNt
TNtTNtf ( ) ( )ttf 03 cos ω=
SOLOFourier Transform of a Signal
Return to Table of contents
SOLO
• Transmitter always on
• Range information can be obtained by modulating EM wave [e.g., frequency modulation (FM), phase modulation (PM)]
• Simple radars used for speed timing, semi-active missile illuminators, altimeters, proximity fuzes.
• Continuous Wave Radar (CW Radar)
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SOLO • Continuous Wave Radar (CW Radar)
The basic CW Radar will transmit an unmodulated (fixed carrier frequency) signal.
( ) [ ]00cos ϕω += tAtsThe received signal (in steady – state) will be.
( ) ( ) ( )[ ]00cos ϕωωα +−+= dDr ttAtsα – attenuation factor
ωD – two way Doppler shiftc
RfRff
fc
DDD
0
/ 22&2
0
−=−===λ
λπω
The Received Power is related to the Transmitted Power by (Radar Equation):
4
1~
RP
P
tr
rcv
One solution is to have separate antennas for transmitting and receiving.
For R = 103 m this ratio is 10-12 or 120 db. This means that we must have a good isolation between continuously transmitting energy and receiving energy.
Basic CW Radar
SOLO • Continuous Wave Radar (CW Radar)
The received signal (in steady – state) ( ) ( ) ( )[ ]002cos ϕπα +−⋅+= dDr ttffAts
We can see that the sign of the Doppler is ambiguous (we get the same result for positiveand negative ωD).
To solve the problem of doppler sign ambiguity we can split the Local Oscillator into two channels and phase shifting theSignal in one by 90◦ (quadrature - Q) with respect to other channel (in-phase – I). Both channels are downconverted to baseband.If we look at those channels as the real and imaginary parts of a complex signal, we get:
has the Fourier Transform: ( ){ } ( ) ( )[ ]DDv ts ωωδωωδπ ++−=F
After being heterodyned to baseband (video band), the signal becomes (after ignoring amplitude factors and fixed-phase terms): ( ) [ ]tts Dv ωcos=
( ) ( ) ( )[ ] tjDDv
Detjtts ωωω2
1sincos
2
1 =+= ( ){ } ( )Dv ts ωωδπ −=2
F
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SOLO • Frequency Modulated Continuous Wave (FMCW)The transmitted signal is: ( ) ( )[ ]00cos ϕθω ++= ttAts
The frequency of this signal is: ( ) ( )
+= t
dt
dtf θω
π 02
1
For FMCW the θ (t) has a linear slope as seen in the figures bellow
Return to Table of contents
SOLO • Frequency Modulated Continuous Wave (FMCW)
The received signal is:
( ) ( ) ( ) ( )[ ]00cos ϕθωωα +−+−+= ddDr ttttAts
α – attenuation factor
ωD – two way Doppler shiftλ
πω Rff DDD
2&2 −==
td – two way time delay
c
Rtd
2=
( ) ( )
−++= dDr ttdt
dfftf θ
π2
10The frequency of received signal is:
λ – mean value of wavelength
Linear Sawtooth Frequency Modulated Continuous Wave
SOLO • Frequency Modulated Continuous Wave (FMCW)
To extract the information we must subtract the received signal frequency fromthe transmitted signal frequency. This is done by mixing (multiplying) those signalsand use a Lower Side-Band Filter to retain the difference of frequencies
( ) ( ) ( ) ( ) ( ) Ddrb fttdt
dt
dt
dtftftf −
−−
=−= θ
πθ
π 2
1
2
1The frequency of mixed signal is:
( ) ( ) ( ) ( )[ ]00cos ϕθωωα +−+−+= ddDr ttttAts
( ) ( )[ ]00cos ϕθω ++= ttAts
( ) ( ) ( ) ( )[ ]
( ) ( ) ( ) ( )[ ]ddD
ddDdr
ttttttA
ttttttAts
−++−+++
−−+−−=
θθωωωα
θθωωα
002
02
cos2
1
cos2
1
Lower Side-BandFilter
Lower SB Filter
Linear Sawtooth Frequency Modulated Continuous Wave
SOLO • Frequency Modulated Continuous Wave (FMCW)
The returned signal has a frequency change due to:
• two way time delayc
Rtd
2=
• two way doppler additionλR
fD
2−=
From Figure above, the beat frequencies fb (difference between transmitted to received frequencies) for a Linear Sawtooth Frequency Modulation are:
Dm
Ddm
b fRTc
fft
T
ff −∆=−∆=+ 4
2/
Dm
Ddm
b fRTc
fft
T
ff −∆−=−∆−=− 4
2/
( )28
−+ −∆
= bbm ff
f
TcR ( )
2
−+ +−= bbD
fff
We have 2 equations with 2 unknowns R and fD
with the solution:
Linear Sawtooth Frequency Modulated Continuous Wave
SOLO• Frequency Modulated Continuous Wave (FMCW)
The Received Power is related to the Transmitted Power by (Radar Equation):
For R = 103 m this ratio is 10-12 or 120 db. This means that we must have a good isolation between continuously transmitting energy and receiving energy.
4
1~
RP
P
tr
rcv
One solution is to have separate antennas for transmitting and receiving.
Linear Sawtooth Frequency Modulated Continuous Wave
SOLO • Frequency Modulated Continuous Wave (FMCW)Linear Sawtooth Frequency Modulated Continuous Wave
Performing Fast Fourier Transform (FFT) we obtain fb+ and fb.
( )28
−+ −∆
= bbm ff
f
TcR
( )2
−+ +−= bbD
fff
From the Doppler Window we get fb+ and fb
-, from which:
SOLO
• Frequency Modulated Continuous Wave (FMCW)
Return to Table of contents
SOLO • Frequency Modulated Continuous Wave (FMCW)
The returned signal has a frequency change due to:
• two way time delayc
Rtd
2=
• two way doppler additionλR
fD
2−=
From Figure above, the beat frequencies fb (difference between transmitted to received frequencies) for a Linear Triangular Frequency Modulation are:
Dm
Ddm
b fRTc
fft
T
ff −∆=−∆=+ 8
4/
positiveslope
Dm
Ddm
b fRTc
fft
T
ff −∆−=−∆−=− 8
4/
negativeslope
( )28
−+ −∆
= bbm ff
f
TcR ( )
2
−+ +−= bbD
fff
We have 2 equations with 2 unknowns R and fD
with the solution:
Linear Triangular Frequency Modulated Continuous Wave
SOLO • Frequency Modulated Continuous Wave (FMCW)Two Targets Detected
Performing FFT for each of the positive, negative and zero slopes we obtain two Beats in each Doppler window.
To solve two targets we can use the Segmented Linear Frequency Modulation.
In the zero slope Doppler window, we obtain the Doppler frequency of the two targets fD1 and fD2.Since , it is easy to find the pair from Positive and Negative Slope Windows that fulfill this condition, and then to compute the respective ranges using:
( )2
−+ +−= bbD
fff
( )28
−+ −∆
= bbm ff
f
TcR
This is a solution for more than two targets.
One other solution that can solve also range and doppler ambiguities is to use manymodulation slopes (Δ f and Tm).
Return to Table of contents
SOLO • Frequency Modulated Continuous Wave (FMCW)
Sinusoidal Frequency Modulated Continuous Wave One of the practical frequency modulations is the Sinusoidal Frequency Modulation.
Assume that the transmitted signal is:
( ) ( )
∆+= tff
ftfAts m
m
ππ 2sin2sin 0
The spectrum of this signal is:
( ) ( )
( )[ ] ( )[ ]{ }
( )[ ] ( )[ ]{ }
( )[ ] ( )[ ]{ }
+
−++
∆+
−++
∆+
−++
∆+
∆=
tfftfff
fJA
tfftfff
fJA
tfftfff
fJA
tff
fJAts
mmm
mmm
mmm
m
32sin32sin
22sin22sin
2sin2sin
2sin
003
002
001
00
ππ
ππ
ππ
πwhere Jn (u) is the Bessel Functionof the first kind, n order and argument u.
Bessel Functions of the first kind
SOLO • Frequency Modulated Continuous Wave (FMCW)
Sinusoidal Frequency Modulated Continuous Wave
Lower Side-BandFilter
( )ts
( )tr
( )tmR
c
ffftffff m
DdmD
tf
b
dm ∆+=∆+≈=< <
+
84
1π
A possible modulating is describe bellow, in which we introduce a unmodulated segmentto measure the doppler and two sinusoidal modulation segments in anti-phase.
From which we obtain:
Rc
ffftffff m
DdmD
tf
b
dm ∆−=∆−≈=< <
−
84
1π
The averages of the beat frequency over one-half a modulating cycle are:
28−+
−∆
= bbmff
f
TcR
2−+
+= bb
D
fff
(must be the same as in unmodulated segment)
Note: We obtaind the same form as for Triangular Frequency Modulated CW
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SOLO
Assume that the transmitter transmits n CW frequencies fi (i=0,1,…,n-1)
Transmitted signals are: ( ) [ ] 1,,1,02sin −== nitfAts iii πThe received signals are: ( ) ( ) ( )[ ]dDiiiii ttffAtr −⋅+= πα 2sin
c
Rt
c
Rf
c
Rfff d
i
jjDi
2,
2210
10 ≈−≈
∆+−≈ ∑
=
where:
1,,2,11 −=∆+= − nifff iii
Since we want to use no more than one antenna for transmitted signals and one antenna for received signals we must have
1,,2,101
−=<<∆∑=
niffi
jj
We can see that the change in received phase Δφi , of two adjacent signals, is related to range R by:
( )c
Rf
c
R
c
Rf
c
Rf
c
Rff
c
Rf i
cR
iiDDii ii
22
222
22
22
22
2
1⋅∆≈⋅⋅∆+⋅∆=⋅−+⋅∆=∆
<<
−πππππϕ
The maximum unambiguous range is given when Δφi=2π :
isunambiguou f
cR
∆=
2
• Multiple Frequency CW Radar (MFCW)
SOLO • Multiple Frequency CW Radar (MFCW)
Return to Table of contents
SOLO • Phase Modulated Continuous Wave (PMCW)
Another way to obtain a time mark in a CW signal is by using Phase Modulation (PM).PMCW radar measures target range by applying a discrete phase shift every T secondsto the transmitted CW signal, producing a phase-code waveform. The returning waveformis correlated with a stored version of the transmitted waveform. The correlation processgives a maximum when we have a match. The time to achieve this match is the time-delaybetween transmitted and receiving signals and provides the required target range.
There are two types of phase coding techniques: binary phase codes and polyphase codes. In the figure bellow we can see a 7-length Barker binary phase code of the transmittedsignal
SOLO • Phase Modulated Continuous Wave (PMCW)
In the figure bellow we can see a 7-length Barker binary phase code of the receivedsignal that, at the receiver, passes a 7-cell delay line, and is correlated to a sampleof the 7-length Barker binary signal sample.
-1 = -1
+1 -1 = 0
-1 +1 -1 = -1
-1 -1 +1-( -1) = 0
+1 -1 -1 –(+1)-( -1) = -1
+1 +1 -1-(-1) –(+1)-1= 0
+1+1 +1-( -1)-(-1) +1-(-1)= 8
+1+1 –(+1)-( -1) -1-( +1)= 0
+1-(+1) –(+1) -1-( -1)= -1
-(+1)-(+1) +1 -( -1)= 0
-(+1)+1-(+1) = -1
+1-(+1) = 0-(+1) = -1
0 = 0
-1-1 -1
Digital CorrelationAt the Receiver the coded pulse enters a7 cells delay lane (from left to right),a bin at each clock.The signals in the cells are summed
clock
123456789
1011121314
+1+1+1+1
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SOLO
PRI – Pulse Repetition Interval PRF – Pulse Repetition Frequency
τ – Pulse Width [μsec]
PRF = 1/PRI
Pulse Duty Cycle = DC = τ / PRI = τ * PRF
Paverrage = DC * Ppeak
Pulse Waveform Parameters
Pulse Radars
• Coherent – Phase is predictable from pulse-to-pulse• Non-coherent – Phase from pulse-to-pulse is not predictable
Range & Doppler Measurements in RADAR SystemsSOLO
( )tf
2
τ2
τ−
A
∞→t
2τ+T
2τ−T
A
2τ+−T
2τ−−T
A
t←∞−
T TA
t
A
t
A
LINEAR FM PULSECODED PULSE
T T
PULSED (INTRAPULSE CODING)
t
( )tf
A
2
τ2
τ−T
AA
T T
A
22
τ+T2
2τ−T
A
T T
A
2τ− 2
τ+T
TN
t
( )tf
A
2
τ2
τ−T
AA
T T
A
22
τ+T2
2τ−T
A
T T
A
2
τ− 2τ+T
TN
PHASE CODED PULSES HOPPED FREQUENCY PULSES
PULSED (INTERPULSE CODING)
t
( )tf
A
T
2/τ−
LOW PRFMEDIUM PRF
PULSED( )tf
T T T T
2/τ+
τ
HIGH PRF
TT T T
A Partial List of the Family of RADAR Waveforms (continue – 1)
Pulses
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SOLOPulse Radars
Return to Table of contents
Coherent Pulse Doppler RadarSOLO
• STALO provides a continuous frequency fLO
• COHO provides the coherent Intermediate Frequency fIF
• Pulse Modulator defines the pulse width the Pulses Rate
Frequency (PRF) number of pulses in a batch • Transmitter/Receiver (T/R) (Circulator) - in the Transmission Phase directs the Transmitted Energy to the Antenna and isolates the Receiving Channel
• IF Amplifier is a Band Pass Filter in the Receiving Channel centered around IF frequency fIF.• Mixer multiplies two sinusoidal signals providing signals with sum or differences of the input frequencies
- in the Receiving Phase directs the Received Energy to the Receiving Channel
21 ff >>
2f
1f21 ff +
21 ff −
Range & Doppler Measurements in RADAR SystemsSOLORadar Waveforms and their Fourier Transforms
Range & Doppler Measurements in RADAR SystemsSOLORadar Waveforms and their Fourier Transforms
Return to Table of contents
SOLO
The basic way to measure the Range to a Target is to send a pulse of EM energy andto measure the time delay between received and transmitted pulse
Range = c td/2
Range Measurements in RADAR Systems
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Run This
SOLO Range & Doppler Measurements in RADAR Systems
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Range Measurement Unambiguity
SOLO
The returned signal from the target located at a range R from the transmitter reaches the receiver (collocated with the transmitter) after
c
Rt
2=
To detect the target, a train of pulses must be transmitted.
PRI – Pulse Repetition Interval PRF – Pulse Repetition Frequency = 1/PRT
To have an unanbigous target range the received pulse must arrive before the transmissionof the next pulse, therefore:
PRFPRI
c
Runabigous 1
2=<
PRF
cRunabigous
2<
Range Measurements in RADAR Systems
Resolving Range Measurement Ambiguity
SOLO
To solve the ambiguity of targets return we must use multiple batches, each with different PRIs (Pulse Repetition Interval). Example: one target, use two batches
First batch: PRI 1 = T1
Target Return = t1-amb
R1_amb=2 c t1_amb
Second batch: PRI 2 = T2
Target Return = t2-amb
R2_amb=2 c t2_amb
To find the range, R, we must solve for the integers k1 and k2 in the equation:
( ) ( )ambamb tTkctTkcR _222_111 22 +=+=We have 2 equations with 3 unknowns: R, k1 and k2, that can be solved becausek1 and k2 are integers. One method is to use the Chinese Remainder Theorem .
For more targets, more batches must be used to solve the Range ambiguity.
See Tildocs # 763333 v1
See Tildocs # 763333 v1
Range Measurements in RADAR Systems
http://www.radartutorial.eu
Resolving Range Measurement Ambiguity
SOLO
In Figure bellow we can see that using a constant PRF we obtain two targets
Target # 1Target # 2
By changing the PRF we can see that Target # 2 is unambiguous
Transmitted Pulse
Range Measurements in RADAR Systems
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SOLODoppler Frequency Shift
( )ωjF
2
NAτ
ω
TNπω 2
0 +
0ω−
TNπω 2
0 −
PRωω +− 0PRωω −− 0
TPR
πω 2=TPR
πω 2=
ω0
TNπω 2
0 +
0ω
TNπω 2
0 −
PRωω +0PRωω −0
TPR
πω 2=TPR
πω 2=
2
2sin
2 τω
τωτ
n
n
NA
PR
PR
( )
( )2
2sin
0
0
NT
NT
ωω
ωω
−
−
( )
( )2
2sin
2
2s in
20
0
NTn
NTn
n
n
NA
RP
RP
PR
PR
ωωω
ωωω
τω
τωτ
−−
−−
( )ωjF
( )02ωωδτ −NA
ω
0ω−PRωω +− 0PRωω −− 0
TPR
πω 2=TPR
πω 2=
ω0
PRωω +0PRωω −0
TPR
πω 2=TPR
πω 2=
2
2sin
2 τω
τωτ
n
n
NA
PR
PR
2
2sin
2 τω
τωτ
n
nNA
PR
PR
0ω PRωω 20 +PRωω 20 −PRωω 20 −−
PRωω 30 −−PRωω 40 −−
PRωω 20 +−
PRωω 30 +− PRωω 40 +−
Fourier Transform of an Infinite Train Pulses
Fourier Transform of an Finite Train Pulses of Lenght N
( )PR
PR
PR
NA ωωωδτω
τωτ
−−
0
2
2sin
2
( ) ( )tAtf 03 cos ω=
t
A A
( )tf1
t
2
τ2
τ−T
A
T T
22
τ+T2
2τ−T
T T
2
τ− 2
τ+T
( )tf 2
t
TN
2/TN2/TN−
( ) ( ) ( ) ( )tftftftf 321 ⋅⋅=Train of Coherent Pulses,of finite length N T,modulated at a frequency 0ω
The pulse coherency is a necessary conditionto preserve the frequency information andto retrieve the Doppler of the returned signal.
Transmitted Train of Coherent Pulses
Range & Doppler Measurements in RADAR Systems
SOLODoppler Frequency Shift
Fourier Transform of an Finite Train Pulses of Lenght N
2
NAτ
ω
TN
πω 20 +
0ω
TN
πω 20 −
PRωω+0PRωω−0
TPR
πω 2=TPR
πω 2=
2NAτ
ω
TN
πω 20 +
0ω
TN
πω 20 −
PRωω+0PRωω−0
TPR
πω 2=TPR
πω 2=
2
2sin
2 τω
τωτ
n
n
NA
PR
PR
( )
( )2
2sin
0
0
NT
NT
ωω
ωω
−
−
2NAτ
ω
TN
πω 20 +
0ω
TN
πω 20 −
PRωω+0PRωω−0
TPR
πω 2=TPR
πω 2=
πω
λ 2&
2P R
DopplerDopple r ftdRd
f <
−=
πω
λ 2&
2PR
Dopple rDopple r ftdRd
f >
−=
Fourier Transform of theTransmitted Signal
Fourier Transform of theReceiveded Signal
with Unambiguous Doppler
Fourier Transform of theReceiveded Signal
with Ambiguous Doppler
Received Train of Coherent Pulses
The bandwidth of a single pulse is usually several order of magnitude greater than theexpected doppler frequency shift 1/τ >> f doppler. To extract the Doppler frequency shift,the returns from many pulses over an observation time T must be frequency analyzed sothat the single pulse spectrum will separate into individual PRF lines with bandwidthsapproximately given by 1/T.
From the Figure we can seethat to obtain an unambiguousDoppler the following conditionmust be satisfied:
PRFc
td
Rdf
td
Rd
f PRMaxMaxdoppler =≤==
πω
λ 2
22 0
or02 f
PRFc
td
Rd
Max
≤
Range & Doppler Measurements in RADAR Systems
SOLO
Coherent Pulse Doppler Radar An idealized target doppler response will provide at IF Amplifier output the signal:
( ) ( )[ ] ( ) ( )[ ]tjtjdIFIF
dIFdIF eeA
tAts ωωωωωω +−+ +=+=2
cos
that has the spectrum:f
fIF+fd-fIF-fd
-fIF fIF
A2/4A2/4 |s|2
0
Because we used N coherent pulses ofwidth τ and with Pulse Repetition Time Tthe spectrum at the IF Amplifier output
f
-fd fd
A2/4A2/4|s|2
0
After the mixer and base-band filter:
( ) ( ) [ ]tjtjdd
dd eeA
tAts ωωω −+==2
cos
We can not distinguish between positive to negative doppler!!!
and after the mixer :
Range & Doppler Measurements in RADAR Systems
SOLO
Coherent Pulse Doppler Radar
We can not distinguish between positive to negative doppler!!!
Split IF Signal:
( ) ( )[ ] ( ) ( )[ ]tjtjdIFIF
dIFdIF eeA
tAts ωωωωωω +−+ +=+=2
cos
( ) ( )[ ]
( ) ( )[ ]tAts
tA
ts
dIFQ
dIFI
ωω
ωω
+=
+=
sin2
cos2
Define a New Complex Signal:
( ) ( ) ( ) ( )[ ]tjQI
dIFeA
tsjtstg ωω +=+=2
ffIF+fd
fIF
A2/2|g|2
0
f
fd
A2/2|s|2
0
Combining the signals after the mixers
( ) tjd
deA
tg ω
2=
We now can distinguish between positive to negative doppler!!!
Range & Doppler Measurements in RADAR Systems
SOLOCoherent Pulse Doppler Radar
Split IF Signal:
( ) ( )[ ]
( ) ( )[ ]tAts
tA
ts
dIFQ
dIFI
ωω
ωω
+=
+=
sin2
cos2
Define a New Complex Signal:
( ) ( ) ( ) ( )[ ]tjQI
dIFeA
tsjtstg ωω +=+=2
ffd
A2/2|s|2
0
Combining the signals after the mixers
( ) tjd
deA
tg ω
2=
We now can distinguish between positive to negative doppler!!!
From the Figure we can see that in this case the doppler is unambiguous only if:
Tff PRd
1=<
Because we used N coherent pulses ofwidth τ and with Pulse Repetition Time Tthe spectrum after the mixer output is
Range & Doppler Measurements in RADAR Systems
SOLO
Coherent Pulse Doppler Radar
Because, for Doppler computation, we used N coherent pulses of width τ and with Pulse Repetition Interval T, the spectrum after the mixer output is
From the Figure we can see that in this case the doppler is unambiguous only if:
Tff PRd
1=<
Range & Doppler Measurements in RADAR Systems
Return to Table of contents
Resolving Doppler Measurement Ambiguity
+=
+= ambDambD f
Tkf
TkV _2
22_1
11
1
2
1
2
λλ
SOLO
To solve the Doppler ambiguity of targets return we must use multiple batches, each with different PRIs (Pulse Repetition Interval). Example: one target, use two batches
First batch: PRI 1 = T1
Target Doppler Return in Range Gate i = fD1-amb
V1_amb=(λ/2) fD1_amb
Range & Doppler Measurements in RADAR Systems
To find the range-rate, V, we must solve for the integers k1 and k2 in the equation:
We have 2 equations with 3 unknowns: V, k1 and k2, that can be solved becausek1 and k2 are integers. One method is to use the Chinese Remainder Theorem .
Second batch: PRI 2 = T2
Target Doppler Return in Range Gate i = fD2-amb
V2_amb=(λ/2) fD2_amb
For more targets, more batches must be used to solve the Doppler ambiguity.
See Tildocs # 763333 v1
See Tildocs # 763333 v1
SOLO Range & Doppler Measurements in RADAR Systems
SOLO Range & Doppler Measurements in RADAR Systems
Return to Table of contents
Range & Doppler Measurements in RADAR SystemsSOLO
Resolution
Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order todistinguish between two different targets.
first targetresponse
second targetresponse
compositetarget
response
greather then 3 db
DistinguishableTargets
first targetresponse
second targetresponse
compositetarget
response
UndistinguishableTargets
less then 3 db
The two targets are distinguishable ifthe composite (sum) of the received signal has a deep (between the twopicks) of at least 3 db.
Return to Table of contents
Range & Doppler Measurements in RADAR SystemsSOLO
Doppler Resolution The Doppler resolution is defined bythe Bandwidth of the Doppler FiltersBWDoppler.
Doppler Dopplerf BW∆ =
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Range & Doppler Measurements in RADAR SystemsSOLO
Angle Resolution
Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order todistinguish between two different targets.
Angle Resolution
RADAR
Target # 1
Target # 2
R
R
3θ
2cos 3θ
R3
3
2sin2 θθ
RR ≈
Angle Resolution is Determined by Antenna Beamwidth.
33
2sin2 θθ
RRRC ≈
=∆
Angle Resolution is considered equivalent to the 3 db Antenna Beamwidth θ3.
The Cross Range Resolution is given by:
Return to Table of contents
SOLO
Unmodulated Pulse Range Resolution Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order todistinguish between two different targets.
Range Resolution
RADAR
τ
c
R
RR ∆+
Target # 1Target # 2
Assume two targets spaced by a range Δ R and a unmodulated radar pulse of τ seconds.
The echoes start to be receivedat the radar antenna at times: 2 R/c – first target 2 (R+Δ R)/c – second target
The echo of the first target endsat 2 R/c + τ
τ τ
time from pulsetransmission
c
R2 ( )c
RR ∆+2τ+
c
R2
ReceivedSignals
Target # 1 Target # 2
The two targets echoes can beresolved if:
c
RR
c
R ∆+=+ 22 τ2
τcR =∆ Pulse Range Resolution
( ) ( ) ≤≤+
=elsewhere
ttAts
0
0cos: 0 τϕω
Range & Doppler Measurements in RADAR Systems
http://www.radartutorial.eu
SOLO
Range Resolution
Range Measurements in RADAR Systems
Run This
http://www.radartutorial.eu
Range Resolution
SOLO Range Measurements in RADAR Systems
Run This
RADAR SignalsSOLO
( ) ( ) ≤≤+
=elsewhere
ttAts
0
0cos: 0 τϕω
Energy( ) ( )
2
2cos22cos1
2
2000
2 ττ
ϕϕτωτ AE
AE ss =⇒
−++=
2
τcR =∆ Pulse Range Resolution
Decreasing Pulse Width Increasing
Decreasing SNR, Radar Performance Increasing
Increasing Range Resolution Capability Decreasing
For the Unmodulated Pulse, there exists a coupling between Range Resolution andWaveform Energy. Return to Table of contents
Pulse Compression WaveformsSOLO
Pulse Compression Waveforms permit a decoupling between Range Resolution and Waveform Energy.
- An increased waveform bandwidth (BW) relative to that achievable with an unmodulated pulse of an equal duration
τ1>>BW
22
τcBW
cR <<=∆
- Waveform duration in excess of that achievable with unmodulated pulse of equivalent waveform bandwidth
BW
1>>τ
PCWF exhibit the following equivalent properties:
This is accomplished by modulating (or coding) the transmit waveform and compressing the resulting received waveform.
SOLO
• Pulse Compression Techniques• Wave Coding
• Frequency Modulation (FM)
- Linear
• Phase Modulation (PM)]
- Non-linear
- Pseudo-Random Noise (PRN)
- Bi-phase (0º/180º)
- Quad-phase (0º/90º/180º/270º)
• Implementation
• Hardware
- Surface Acoustic Wave (SAW) expander/compressor
• Digital Control- Direct Digital Synthesizer (DDS)
- Software compression “filter”
SOLO
• Pulse Compression Techniques
SOLO
• Pulse Compression Techniques
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SOLO
Linear FM Modulated Pulse (Chirp)
( ) ( )2/cos 203 ttAtf ωω ∆+=
t
A
2/τ−2/τ ( )
222cos
2
0
ττµω ≤≤−
+= tt
tAtsi
Pulse Compression Waveforms
Linear Frequency Modulation is a technique used to increase the waveform bandwidthBW while maintaining pulse duration τ, such that
BW
1>>τ 1>>⋅BWτ
222 0
2
0
ττµωµωω ≤≤−+=
+= tt
tt
td
d
Matched Filters for RADAR Signals
( ) ( )( ) ( )
≤≤−== −∗
Ttttsth
eSH
i
tji
00
0ωωω
SOLO
The Matched Filter (Summary(
si (t) - Signal waveform
Si (ω) - Signal spectral density
h (t) - Filter impulse response
H (ω) - Filter transfer function
t0 - Time filter output is sampled
n (t) - noise
N (ω) - Noise spectral density
Matched Filter is a linear time-invariant filter hopt (t) that maximizesthe output signal-to-noise ratio at a predefined time t0, for a given signal si (t(.
The Matched Filter output is:
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) 00
00
tjiii
iii
eSSHSS
dttssdthsts
ωωωωωω
ξξξξξξ
−∗
+∞
∞−
+∞
∞−
⋅=⋅=
+−=−= ∫∫
SOLO
Linear FM Modulated Pulse (continue – 1)
Pulse Compression Waveforms
Concept of Group Delay
BW
1>>τ
τ
BW
1
( )222
cos2
0
ττµω ≤≤−
+= tt
tAtsi
( ) ( )222
cos2
0
00 ττµω ≤≤−
−=−=
=
tt
tAtsth i
t
MF
Matched Filter
( )tsi ( )tso
( ) ( )tsth i
t
MF −==00 ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )ωωωωω
ξξξξξξ
∗=
+∞
∞−
=+∞
∞−
⋅=⋅=
−=−= ∫∫
ii
t
i
ii
t
i
SSHSS
dtssdthsts
0
0
0
0
0
0
SOLO
Linear FM Modulated Pulse (continue – 7)
Pulse Compression Waveforms
Linear FM Modulated Pulse (Chirp) Summary
• Chirp is one of the most common type of pulse compression code
• Chirp is simple to generate and compress using IF analog techniques, for example, surface acoustic waves (SAW) devices.
• Large pulse compression ratios can be achieved (50 – 300).
• Chirp is relative insensitive to uncompressed Doppler shifts and can be easily weighted for side-lobe reduction.
• The analog nature of chirp sometimes limits its flexibility.
• The very predictibility of chirp mades it asa poor choice for ECCM purpose.
Return to Table of Contents
SOLOPulse Compression Techniques
Phase CodingA transmitted radar pulse of duration τ is divided in N sub-pulses of equal durationτ’ = τ /N, and each sub-pulse is phase coded in terms of the phase of the carrier.
The complex envelope of the phase codedsignal is given by:
( ) ( ) ( )∑−
=
−=1
02/1 '
'
1 N
nn ntu
Ntg τ
τ where:
( ) ( ) ≤≤
=elsewhere
tjtu n
n 0
'0exp τϕ
Pulse Compression Techniques
Return to Table of Contents
SOLO
Example: Pulse poly-phase coded of length 4
Given the sequence: { } 1,,,1 −−++= jjck
which corresponds to the sequence of phases 0◦, 90◦, 270◦ and 180◦, the matched filter is given in Figure bellow.
{ } 1,,,1* −+−+= jjck
Pulse Compression Techniques
Pulse poly-phase coded of length 4
At the Receiver the coded pulse enters a 4 cells delay lane (from left to right), a bin at each clock.The signals in the cells are multiplied by -1,+j,-j or +1 and summed.
clock
SOLOPoly-Phase Modulation
-1 = -11 1+
-j +j = 02 1+j+
+j -1-j = -13 1+j+j−
+1 +1+1+1 = 44 1+j+j−1−
-j-1+j = -15 j+j−1−
+j - j = 06
j−1−7
1− -1 = -1
8 0
Σ
{ } 1,,,1 −−++= jjck
1− 1+j+ j− {ck*}
0 = 00
0
1
2
3
4
5
6
7
{ } 1,,,1* −+−+= jjck
Run This
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SOLO Pulse Compression Techniques
Bi-Phase Codes
• easy to implement
• significant range sidelobe reduction possible
• Doppler intolerant
A bi-phase code switches the absolute phase of the RF carrier between two states180º out of phase.
Bandwidth ~ 1/τ
Transmitted Pulse
Received Pulse
• Peak Sidelobe Level
PSL = 10 log (maximum side-lobe power/ peak response power)
• Integrated Side-lobe Level
ISL = 10 log (total power in the side-lobe/ peak response power)
Bi-Phase Codes Properties
The most known are the Barker Codes sequence of length N, with sidelobes levels, atzero Doppler, not higher than 1/N.
SOLO Pulse Compression Techniques
Bi-Phase Codes
LengthN
Barker Code PSL(db)
ISL(db)
2 + - - 6.0 - 3.0
2 + + - 6.0 - 3.0
3 + + - - 9.5 - 6.5
3 + - + - 9.5 - 6.5
4 + + - + - 12.0 - 6.0
4 + + + - - 12.0 - 6.0
5 + + + - + - 14.0 - 8.0
7 + + + - - + - - 16.9 - 9.1
11 + + + - - - + - - + - - 20.8 - 10.8
13 + + + + + - - + + - + - + - 22.3 - 11.5
Barker Codes-Perfect codes –Lowest side-lobes forthe values of N listed in the Table.
Pulse bi-phase Barker coded of length 7
Digital CorrelationAt the Receiver the coded pulse enters a7 cells delay lane (from left to right),a bin at each clock.The signals in the cells are multipliedby ck* and summed.
clock
-1 = -11
+1 -1 = 02
-1 +1 -1 = -13
-1 -1 +1-( -1) = 04
+1 -1 -1 –(+1)-( -1) = -15
+1 +1 -1-(-1) –(+1)-1= 06
+1+1 +1-( -1)-(-1) +1-(-1)= 77
+1+1 –(+1)-( -1) -1-( +1)= 08
+1-(+1) –(+1) -1-( -1)= -19
-(+1)-(+1) +1 -( -1)= 010
-(+1)+1-(+1) = -111
+1-(+1) = 012-(+1) = -113
0 = 014
SOLO Pulse Compression Techniques
-1-1 -1+1+1+1+1 { }*kc
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SOLO Pulse Compression TechniquesBi-Phase Codes
Combined Barker CodesOne scheme of generating codes longer than 13 bits is the method of forming combinedBarker codes using the known Barker codes. For example to obtain a 20:1 pulsecompression rate, one may use eithera 5x4 or a 4x5 codes.
The 5x4 Barker code (see Figure) consists of the 5 Barker code, each bit of which is the 4-bit Barker code. The 5x4 combined code is the 20-bit code.
• Barker Code 4
• Barker Code 5
SOLO Pulse Compression TechniquesBi-Phase Codes
SOLO Pulse Compression TechniquesBi-Phase Codes
Binary Phase Codes Summary
• Binary phase codes (Barker, Combined Barker) are used in most radar applications.
• Binary phase codes can be digitally implemented. It is applied separately to I and Q channels.
• Binary phase codes are Doppler frequency shift sensitive.
• Barker codes have good side-lobe for low compression ratios.
• At Higher PRFs Doppler frequency shift sensitivity may pose a problem.
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SOLO Pulse Compression TechniquesPoly-Phase Codes
Frank Codes
In this case the pulse of width τ is divided in N equal groups; each group issubsequently divided into other N sub-pulses each of width τ’. Therefore thetotal number of sub-pulses is N2, and the compression ratio is also N2.
A Frank code of N2 sub-pulses is called a N-phase Frank code. The fundamentalphase increment of the N-phase Frank code is: N/360=∆ ϕ
For N-phase Frank code the phase of each sub-pulse is computed from:
( )
( ) ( ) ( ) ( )
ϕ∆
−−−−
−−
21131210
126420
13210
00000
NNNN
N
N
Each row represents the phases of the sub-pulses of a group
SOLO Pulse Compression TechniquesPoly-Phase Codes
Frank Codes (continue – 1)
Example: For N=4 Frank code. The fundamental phase increment of the 4-phase Frank code is: 904/360 ==∆ ϕ
We have:
−−−−−−
⇒
→
jj
jjj
formcomplex
11
1111
11
1111
901802700
18001800
270180900
0000
90
Therefore the N = 4 Frank code has the following N2 = 16 elements
{ }jjjjF 11111111111116 −−−−−−=
The phase increments within each row represent a stepwise approximation of an up-chirp LFM waveform.
SOLO Pulse Compression TechniquesPoly-Phase Codes
Frank Codes (continue – 2)
Example: For N=4 Frank code (continue – 1).
If we add 2π phase to the third N=4 Frank phase row and 4π phase to the forth(adding a phase that is a multiply of 2π doesn’t change the signal) we obtain aanalogy to the discrete FM signal.
If we use then the phases of the discrete linear FM and the Frank-coded signals are identical at all multipliers of τ’.
'/1 τ=∆ f
SOLO Pulse Compression TechniquesPoly-Phase Codes
Frank Codes (continue – 4)
Fig. 8.8 Levanon pg.158,159
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SOLO
Pseudo-Random Codes
Pseudo-Random Codes are binary-valued sequences similar to Barker codes.
The name pseudo-random (pseudo-noise) stems from the fact that they resemblea random like sequence.
The pseudo-random codes can be easily generated using feedback shift-registers.
It can be shown that for N shift-registers we can obtain a maximum length sequenceof length 2N-1.
0 1 0 0 1 1 123-1=7
Register# 1
Register# 2
Register# 3
XOR
clock
A
B
Input A Input B Output XOR
0 0 0 0 1 1 1 0 1 1 1 0
Register # 1
Register # 2
Register # 3
0 1 0 sequence
I.C.
0 0 1 1
1 0 0 2
1 1 0 3
1 1 1 4
0 1 1 5
1 0 1 60 1 0 7
clock
0 0 1 8
0
Pulse Compression Techniques
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SOLO
Pseudo-Random Codes (continue – 1)To ensure that the output sequence from a shift register with feedback is maximal length, the biths used in the feedback path like in Figure bellow, must be determined by the 1 coefficients of primitive, irreducible polynomials modulo 2. As an example for N = 4, length 2N-1=15, can be written in binary notation as 1 0 0 1 1.
The primitive, irreductible polynomial that this denotes is (1)x4 + (0)x3 + (0)x2 + (1)x1 + (1)x0
1 0 0 1 0 0 0 1 1 1 1 0 1 0 1
24-1=15
sequence
1 0 0 1 I.C.0
The constant (last) 1 term in every such polynomial corresponds to the closing of the loop to the first bit in the register.
Register# 1
Register# 2
Register# 3
XOR
clock
AB
Input A Input B Output XOR
0 0 0 0 1 1 1 0 1 1 1 0
Register# 4
Register # 1
Register # 2
Register # 3clock
Register # 4
1 0 1 0 0
0 0 1 0 2
0 0 0 1 3
1 0 0 0 4
1 1 0 0 5
1 1 1 0 6
1 1 1 1 7
0 1 1 1 8
1 0 1 1 9
0 1 0 1 10
1 0 1 0 11
1 1 0 1 12
0 1 1 0 13
0 0 1 1 14
1 0 0 1 15
0 1 0 0 16
0 0 1 017
Pulse Compression Techniques
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SOLO
Pseudo-Random Codes (continue – 2)
Pulse Compression Techniques
Input A Input B Output XOR
0 0 0 0 1 1 1 0 1 1 1 0
Register# 1
Register# 2
Register# n
XOR
clock
AB
Register# (n-1)
Register# m
. . .. . .
2 3 1 2 ,1
3 7 2 3 ,2
4 15 2 4 ,3
5 31 6 5 ,3
6 63 6 6 ,5
7 127 18 7 ,6
8 255 16 8 ,6 ,5 ,4
9 511 48 9 ,5
10 1,023 60 10 ,7
11 2,047 176 11 ,9
12 4,095 144 12 ,11 ,8 ,6
13 8,191 630 13 ,12 ,10 ,9
14 16,383 756 14 ,13 ,8 ,4
15 32,767 1,800 15 ,14
16 65,535 2,048 16 ,15 ,13 ,4
17 131,071 7,710 17 ,4
18 262,143 7,776 18 ,11
19 524,287 27,594 19 ,18 ,17 ,14
20 1,048,575 24,000 20 ,17
Number ofStages n
Length ofMaximal Sequence N
Number ofMaximal Sequence M
Feedback stageconnections
Maximum Length Sequence
n – stage generator
N – length of maximum sequence
12 −= nNM – the total number of maximal-length sequences that may be obtained from a n-stage generator
∏
−=
ipN
nM
11
where pi are the prime factors of N.
SOLO
Pseudo-Random Codes (continue – 3)
Pulse Compression Techniques
Pseudo-Random Codes Summary
• Longer codes can be generated and side-lobes eventually reduced.
• Low sensitivity to side-lobe degradation in the presence of Doppler frequency shift.
• Pseudo-random codes resemble a noise like sequence.
• They can be easily generated using shift registers.
• The main drawback of pseudo-random codes is that their compression ratio is not large enough.
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SOLO Waveform Hierarchy• Pulse Compression Techniques
SOLO Coherent Pulse Doppler Radar
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SOLO
• Stepped Frequency Waveform (SFWF)
The Stepped Frequency Waveform is a Pulse Radar System technique for obtaining high resolution range profiles with relative narrow bandwidth pulses.
• SFWF is an ensemble of narrow band (monochromatic) pulses, each of which is stepped in frequency relative to the preceding pulse, until the required bandwidth is covered.
• We process the ensemble of received signals using FFT processing.
• The resulting FFT output represents a high resolution range profile of the Radar illuminated area.
• Sometimes SFWF is used in conjunction with pulse compression.
SOLO
• Stepped Frequency Waveform (SFWF)
SOLO
• Pulse Compression Techniques
SOLO
• Steped Frequency Waveform (SFWF)
SOLO
SOLO
SOLO RF Section of a Generic Radar
Antenna – Transmits and receives Electromagnetic Energy
T/R – Isolates between transmitting and receiving channels
REF – Generates and Controls all Radar frequencies
XMTR – Transmits High Power EM Radar frequencies
RECEIVER – Receives Returned Radar Power, filter itand down-converted to Base Band fordigitization trough A/D.
Power Supply – Supplies Power to all Radar components.
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SOLO Radar Configuration
AntennaAntenna performs the following essential functions:
• It transfers the transmitter energy to signals in space with the required distribution and efficiency. This process is applied in an identical way on reception.
• It ensures that the signal has the required pattern in space. Generally this has to be sufficiently narrow to provide the required angular resolution and accuracy.
• It has to provide the required time-rate of target position updates. In the case of a mechanically scanned antenna this equates to the revolution rate. A high revolution rate can be a significant mechanical problem given that a radar antenna in certain frequency bands can have a reflector with immense dimensions and can weigh several tons.
The antenna structure must maintain the operating characteristics under all environmental conditions. Radomes (Radar Domes) are generally used where relatively severe environmental conditions are experienced.
• It must measure the pointing direction with a high degree of accuracy.
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SOLO Radar Configuration
Antenna pattern Figure 1: Antenna pattern in a polar-coordinate graph
Figure 2: The same antenna pattern in a rectangular-coordinate graph
Most radiators emit (radiate) stronger radiation in one direction than in another. A radiator such as this is referred to as anisotropic. However, a standard method allows the positions around a source to be marked so that one radiation pattern can easily be compared with another.
The energy radiated from an antenna forms a field having a definite radiation pattern. A radiation pattern is a way of plotting the radiated energy from an antenna. This energy is measured at various angles at a constant distance from the antenna. The shape of this pattern depends on the type of antenna used.
Antenna Gain Independent of the use of a given antenna for transmitting or receiving, an important characteristic of this antenna is the gain. Some antennas are highly directional; that is, more energy is propagated in certain directions than in others. The ratio between the amount of energy propagated in these directions compared to the energy that would be propagated if the antenna were not directional (Isotropic Radiation) is known as its gain. When a transmitting antenna with a certain gain is used as a receiving antenna, it will also have the same gain for receiving.
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SOLO Antenna
Beam Width
Figure 1: Antenna pattern in a polar-coordinate graph
Figure 2: The same antenna pattern in a rectangular-coordinate graph
The angular range of the antenna pattern in which at least half of the maximum power is still emitted is described as a „Beam With”. Bordering points of this major lobe are therefore the points at which the field strength has fallen in the room around 3 dB regarding the maximum field strength. This angle is then described as beam width or aperture angle or half power (- 3 dB) angle - with notation Θ (also φ). The beam width Θ is exactly the angle between the 2 red marked directions in the upper pictures. The angle Θ can be determined in the horizontal plane (with notation ΘAZ) as well as in the vertical plane (with notation ΘEL).
Major and Side Lobes (Minor Lobes)
The pattern shown in figures has radiation concentrated in several lobes. The radiation intensity in one lobe is considerably stronger than in the other. The strongest lobe is called major lobe; the others are (minor) side lobes. Since the complex radiation patterns associated with arrays frequently contain several lobes of varying intensity, you should learn to use appropriate terminology. In general, major lobes are those in which the greatest amount of radiation occurs. Side or minor lobes are those in which the radiation intensity is least.
http://www.radartutorial.eu
Radar Antenae for Different Frequency Spectrum
SOLO Antenna
Summary Radar Antennae
1. A radar antenna is a microwave system, that radiates or receives energy in the form of electromagnetic waves.
2. Reciprocity of radar antennas means that the various properties of the antenna apply equally to transmitting and receiving.
3. Parabolic reflectors („dishes”) and phased arrays are the two basic constructions of radar antennas.
4. Antennas fall into two general classes, omni-directional and directional.
• Omni-directional antennas radiate RF energy in all directions simultaneously. • Directional antennas radiate RF energy in patterns of lobes or beams that extend outward from the antenna in one direction for a given antenna position.
5. Radiation patterns can be plotted on a rectangular- or polar-coordinate graph. These patterns are a measurement of the energy leaving an antenna.
• An isotropic radiator radiates energy equally in all directions. • An anisotropic radiator radiates energy directionally. • The main lobe is the boresight direction of the radiation pattern. • Side lobes and the back lobe are unwanted areas of the radiation pattern.
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r
MAXr
S
SG =:
Antenna
BϕBϑ
ϕD
ϑD
Antenna
RadiationBeam
Assume for simplicity that the Antenna radiates all the power into the solid angledefined by the product , where and are the angle from the boresight at which the power is half the maximum (-3 db).
BB ϕϑ , 2/Bϕ± 2/Bϑ±
ϑϑ
λη
ϑDB
1=ϕϕ
λη
ϕDB
1=
λ - wavelength
ϕϑ DD , - Antenna dimensions in directionsϕϑ,
ϕϑ ηη , - Antenna efficiency in directionsϕϑ,
then ( ) effBB
ADDG22
444
λπηη
λπ
ϕϑπ
ϕϑϕϑ ==⋅
=
whereϕϑϕϑ ηη DDAeff =:
is the Effective Area of the Antenna.
2
4
λπ=
effA
G
SOLO
Antenna Gain
Antenna
Transmitter
IV
Receiver
R
1 2
Let see what is the received power on an Antenna, with an effective area A2 and range R from the transmitter, with an Antenna Gain G1
Transmitter
VI
Receiver
R
1 2
2122 4AG
R
PASP dtransmitte
rreceived π==
Let change the previous transmitter into a receiver and the receiver into a transmitter that transmits the same power as previous. The receiver has now an Antenna with an effective area A1 . The Gain of the transmitter Antenna is now G2.
According to Lorentz Reciprocity Theorem the same power will be received by the receiver; i.e.:
1224AG
R
PP dtransmittereceived π
=therefore
1221 AGAG =or
constA
G
A
G ==2
2
1
1
We already found the constant; i.e.: 2
4
λπ=
A
G
SOLO
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AntennaSOLO
There are two types of antennas in modern fighters
1. Mechanically Scanned Antenna (MSA)
In this case the antenna is gimbaled and antenna servo is used to move theantenna (and antenna beam) in azimuth and elevation.
For target angular position, relative to antenna axis two methods are used:
• Conical scan of the antenna beam relative to antenna axis (older technique)
• Monopulse antenna beam where the antenna is divided in four quadrantsand the received signal of those quadrants is processed to obtain thesum (Σ) and differences in azimuth and elevation (ΔEl, ΔAz) areprocessed separately (modern technique)
2. Electronic Scanned Antenna (ESA)
The antenna is fixed relative to aircraft and the beam is electronically steered inazimuth and elevation relative to antenna (aircraft) axis. Two types are known:
• Passive Electronic Scanned Array (PESA)
• Active Electronic Scanned Array (AESA) with Transmitter and Receiver (T/R) elements on the antenna.
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SOLO
SOLO Airborne Radars
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SOLO Airborne Radars
Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998
1. Mechanically Scanned Antenna (MSA)
Conically Scanned Antenna
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Conical scan radar
SOLO Conical Scan Angular Measurement
http://www.radartutorial.eu
Conical Scan Angular Measurement
Target Angle φ Detector
Conical Scan Angular Measurement
ERROR DETECTION CONTROL-SCAN RADARERROR DETECTION CONTROL-SCAN RADAR
CONTROL-SCAN TRACKINGCONTROL-SCAN TRACKING CONTROL-SCAN BEAM RELATIONSHIPSCONTROL-SCAN BEAM RELATIONSHIPS
ENVELOPE OF PULSESENVELOPE OF PULSES
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SOLO Airborne Radars
Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998
Monopulse antenna
1. Mechanically Scanned Antenna (MSA)
http://www.radartutorial.eu
Monopulse Angle Measurement
SOLO
Monopulse Angular Track
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SOLO
Electronically Scanned Array (ESA)
Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998
SOLO Airborne Radars
Electronically Scanned Array
SOLO Airborne Radars
Electronically Scanned Array
Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998http://www.ausairpower.net/APA-Zhuk-AE-Analysis.html
SOLO Airborne RadarsElectronic Scanned Antenna
Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998
SOLO Airborne Radars
http://www.acq.osd.mil/dsb/reports/hfradar.pdf
SOLO Airborne Radars
SOLO Airborne Radars
http://www.acq.osd.mil/dsb/reports/hfradar.pdf
SOLO Antenna
SOLO Antenna
SOLOAntenna
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SOLORadar Basic
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Continue toRadar Basic- Part II
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TechnionIsraeli Institute of Technology
1964 – 1968 BSc EE1968 – 1971 MSc EE
Israeli Air Force1970 – 1974
RAFAELIsraeli Armament Development Authority
1974 – 2013
Stanford University1983 – 1986 PhD AA
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